# PGP-Clinical-TimeKAN: Prior-Guided Joint Probabilistic Forecasting of Clinical Trajectories

arXiv: https://arxiv.org/abs/2609.05488 · HTML: https://mlsanity.com/paper/2609.05488/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 38 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 23 of 23)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Kolmogorov-Arnold Graph Neural Networks](https://mlsanity.com/paper/2406.18354/) (2024)
- [TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting](https://mlsanity.com/paper/2502.06910/) (2025)
- [Deep Reinforcement Learning Framework for Thoracic Diseases Classification via Prior Knowledge Guidance](https://mlsanity.com/paper/2306.01232/) (2023)
- [Temporal-spatial Correlation Attention Network for Clinical Data Analysis in Intensive Care Unit](https://mlsanity.com/paper/2306.01970/) (2023)

## Abstract (arXiv)

Clinical deterioration unfolds through coupled, partially observed trajectories, not a single diagnostic label. We introduce PGP-Clinical-TimeKAN, a trajectory-first framework for joint probabilistic forecasting of multivariate physiology. It combines missingness-aware temporal encoders, a soft organ-system prior, patient-specific relations, nonlinear Kolmogorov-Arnold messages, and a low-rank multivariate Student-t head. We evaluate 24-hour histories and six-hour forecasts on a frozen MIMIC-IV-derived cohort of 6,882 patients and 54,694 windows. Across five seeds and 13 models, PGP-Clinical-TimeKAN obtains the second-lowest normalized MAE (0.37727 +/- 0.00029) and the lowest RMSE (0.52656 +/- 0.00034). It reduces MAE by 0.52% relative to deterministic TimeKAN. For probabilistic forecasting, it reaches a marginal NLL of 0.66380 and a CRPS of 0.27301. Empirical coverage is 0.533, 0.831, and 0.958 for nominal 50%, 80%, and 95% intervals. Removing relational structure causes the largest ablation loss. Increasing covariance rank improves joint likelihood but has little effect on point accuracy. A trajectory-derived risk score remains weaker than a dedicated GRU-D classifier (AUROC 0.603 versus 0.650), which limits the present clinical claim. Joint trajectory forecasting therefore provides an inspectable intermediate task, but accurate physiology forecasts alone do not ensure a calibrated event detector.